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Math Help - World Problem dealing with matrices

  1. #1
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    Oct 2008
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    Question World Problem dealing with matrices

    Please help me to understand this problem, if I understand how to set it up I know I can solve it. . .

    Problem: Candidate A and candidate B are running for mayor of a small town. After attending a debate, some citizens change their minds about the candidate for whom they will vote. Let m = 25% be the percent of citizens that switch from candidate A to candidate B. Let n = 16% be the percent of citizens that switch from candidate B to candidate A. Before the debate, candidate A was expected to win the election 1200 votes to 950 votes. After the debate, how many vots will candidate A and candidate B recieve? Use the transition matrix T to help you answer the question.

    [1-m n] = T
    [ m 1-n]


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  2. #2
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    Sep 2008
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    Halifax, Nova Scotia
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     <br />
\left(\begin{array}{cc}1-.25&.16\\.25& 1-.16\end{array}\right)<br />
    then
    <br />
\left(\begin{array}{cc}.75&.16\\.25& .84\end{array}\right) = T
    so
    \left(\begin{array}{cc}.75&.16\\.25& .84\end{array}\right) \left(\begin{array}{cc}1200\\950\end{array}\right)
    when multiplied out we get
    \left(\begin{array}{cc}952\\1245.8\end{array}\righ  t)
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